To calculate the amount after 8 years with 7% interest, we'll use the formula for compound interest. The formula is:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for in years.

If the interest is compounded annually (once per year), $ n = 1 $.

Given:
- $ P = 6709 $
- $ r = 0.07 $ (7% interest)
- $ n = 1 $ (compounded annually)
- $ t = 8 $ years

Plugging these values into the formula:

\[
A = 6709 \left(1 + \frac{0.07}{1}\right)^{1 \times 8}
\]

\[
A = 6709 \times (1.07)^8
\]

Now, let's calculate $ A $:

\[
A = 6709 \times 1.718186
\]

\[
A \approx 11526.41
\]

So, after 8 years, the amount will be approximately **$11,526.41**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the total amount change if the interest was compounded quarterly instead of annually?
2. What would be the amount if the interest rate was 5% instead of 7%?
3. How much interest is earned in the first year alone?
4. What is the difference in total amount if the investment period is reduced to 5 years?
5. How would you calculate the present value if you wanted to achieve a specific amount in 8 years at 7% interest?

**Tip:** Always verify if the interest is compounded annually or at a different frequency to use the correct value of $ n $ in the formula.

Learn how to calculate compound interest with a 7% annual interest rate over 8 years on an initial principal of $6709. Follow a step-by-step solution using the compound interest formula. Explore variations like quarterly compounding and different interest rates.

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